# Homework Help: Linear Algebra vector

1. Jan 17, 2009

### sdoyle

1. The problem statement, all variables and given/known data

The line l passes through the point P=(1,-1,1) and has direction vector d=[2,3,-1]. Determine whether l and P are parallel, perpendicular, or neither to 2x+3y-z=1.

2. Relevant equations
n.p=n.x, cross product, dot product

3. The attempt at a solution
Would you just relate the direction vector, d, to the normal vector, n[2,3,-1] ?

2. Jan 17, 2009

### Dick

Yes, you would just relate the normal vector to the direction vector. How do they relate?

3. Jan 17, 2009

### sdoyle

they would be parallel because they are scalar multiples of one another (1 is the multiple) also the cross product would be zero indicating parallel vectors.

4. Jan 17, 2009

### Dick

That means that the NORMAL to the plane is parallel to the line. So what's the relation between the line and the plane?

5. Jan 17, 2009

### sdoyle

that they are perpendicular?

6. Jan 17, 2009

### Dick

Yes, they are.

7. Jan 17, 2009

### sdoyle

How would you prove that mathematically?

8. Jan 17, 2009

### Dick

What's to prove? The normal vector of the plane is parallel to the line. You proved that by showing they are scalar multiples or using the cross product. You're done.